82 THE MAGNETIC CIRCUIT [ART. 33 



lengths of the equivalent air-gap, the number of additional ampere- 

 turns is calculated according to the formula aB m / p, and then is 

 multiplied by the number of joints in series (usually four). This 

 number of ampere-turns must be added to M m calculated above. 

 The energy component i\ of the exciting current is determined 

 [mm the power lost in hysteresis and eddy currents in the core. 

 Having calculated this power P as is explained in Article 19, we 

 find ii = P/Ei, where E\ is the primary applied voltage. Knowing 

 i,, and 1*1, the total no-load current is found as their geometric .sum, 



The watts expended in core loss depend only upon the volume 

 of the iron, the frequency, and the flux density used. It can be 

 also shown that the reactive volt-amperes required for the excita- 

 tion of the magnetic circuit of a transformer depend only upon the 

 volume of the iron, the frequency, and the flux density. Namely, 

 neglecting the influence of the joints, eq. (41) can be written in the 

 form 



Eq. (28) in Art. 25 can be written as 



where A is the cross-section of the iron, and B m is the maximum 

 flux density, in kilolines per square centimeter. Multiplying these 

 two equations together, term by term, and cancelling HI we get, 

 after reduction, 



E l i /V=7ifB m H m XlQ- 5 , .... (42) 



where V=Al is the volume of the iron, in cubic centimeters. 

 The left-hand side of eq. (42) represents the reactive magnetizing 

 volt-amperes per unit volume of iron; the right-hand side is a 

 function of / and B m only, because H m can be expressed through 

 B m from the magnetization curve of the material. 



Formula (42) can be plotted as a set of curves, one for each 

 commercial frequency. These curves are quite convenient in the 

 design of transformers, because they enable one to estimate 

 directly either the permissible volume of iron, or the permissible 

 flux density, when the reactive component of the exciting cur- 



density from 60 to 80 ampere-turns. At other flux densities the increase 

 is proportional. 



